已知x=（根号20-4）/2求x^2+1/x^2

Question

已知 x=（根号20-4）/2 求x^2+1/x^2

Answer 1

x=（根号20-4）/2=（2根号5-4）2= 根号5 -2
1/x=1/（根号5-2）= （根号5+2)/(5-4) = 根号5 +2
x^2+1/x^2=（根号5-2)^2 + (根号5+2)^2 = 5+4-4根号5+5+4+4根号5=18